4.2 Find the z-transform of each of the following sequences: (a) x(n) = 38(n)+ 8(n - 2) + 8(n + 2) (b) x(n) = u(n) – u(n – 10) %3D

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4.2
Find the z-transform of each of the following sequences:
(a) x(n) = 38(n)+ 8(n – 2) + 8(n + 2)
Cauchy's integral theorem may be used to show that the coefficients x(n) may be found from X(z) as follows:
(b) x(n) = u(n) – u(n – 10)
x(n) =
(a) x(2) = 3+ z-2 + z?
2n i X(2)2"-d=:
Jc
1-z-10
Now let:
(b)
X(2) =
1-:-1
X(z) =
z - 0.2
Then:
4.23
Find the inverse of each of the following 2-transforms:
1
z"
dz
j2n J z- 0,2
(b) X(z) =
Iz| > !
1-
According to Cauchy integral:
x(n) = (})"u(n) + 3()"u(n)
1
f(z)
f(a)
dz
a
x[n] = 0.2"
Transcribed Image Text:4.2 Find the z-transform of each of the following sequences: (a) x(n) = 38(n)+ 8(n – 2) + 8(n + 2) Cauchy's integral theorem may be used to show that the coefficients x(n) may be found from X(z) as follows: (b) x(n) = u(n) – u(n – 10) x(n) = (a) x(2) = 3+ z-2 + z? 2n i X(2)2"-d=: Jc 1-z-10 Now let: (b) X(2) = 1-:-1 X(z) = z - 0.2 Then: 4.23 Find the inverse of each of the following 2-transforms: 1 z" dz j2n J z- 0,2 (b) X(z) = Iz| > ! 1- According to Cauchy integral: x(n) = (})"u(n) + 3()"u(n) 1 f(z) f(a) dz a x[n] = 0.2"
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